Spin effects in gravitational radiation backreaction III. Compact binaries with two spinning components

TL;DR

The paper addresses gravitational radiation backreaction for eccentric binaries with two spinning components, incorporating spin-orbit and spin-spin effects up to $3/2$ PN in both dynamics and radiation. It develops a dual-tool approach using the generalized eccentric anomaly $\xi$ and true anomaly $\chi$ parametrizations and the residue theorem to obtain secular evolution equations, yielding both instantaneous and averaged losses for energy $E$, orbital angular momentum $L$, and spin angles. A key finding is that orbital eccentricity accelerates the evolution of spin orientations, with complete evolution equations provided in two equivalent forms: $(E,L,\text{angles})$ and $(a,e,\kappa_i)$. The framework unifies prior one-spin and Lense-Thirring results and enables accurate gravitational-wave templates for eccentric, spinning binaries, including two-spin couplings and their impact on waveform modulation.

Abstract

The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of the spin and orbital angular momenta reveal a speed-up effect due to the eccentricity. The dissipative evolutions of the relevant dynamical and angular variables is presented in the form of a closed system of differential equations.

Figures (1)

• Figure 1: The angles subtended by ${\bf \hat{L}_N}$ and ${\bf \hat{S}_i}$ , and the difference $\Delta\psi$ of the angles subtended by the node line and the spin projections on the plane of orbit. To leading order, the Newtonian angular momentum ${\bf L_N=L}$. These angles are related by the spherical triangle identity. $\psi$ and $\psi_0$ are the respective angles of the position ${\bf r}$ and the direction of the periastron with the node line.